Question

Assume each of the following bonds have 10-year maturities, and the coupons are paid an- nually. Which of the following bonds offers the highest yield to maturity? Which offers the lowest? Which offers the highest and lowest duration? (A) Bond A with a coupon of 2% selling for a discount of 81.62% (B) Bond B with a coupon of 4% selling for a discount of 98.39% (C) Bond C with a coupon of 8% selling for a premium of 133.42%

Answer 1

Bond A

YTM is calculated using RATE function in Excel :

nper = 10 (years remaining until maturity with 1 annual coupon payment each year)

pmt = 100 * 2% (annual coupon payment = face value * coupon rate)

pv = -81.62 (Current price of bond. This is entered with a negative sign because it is a cash outflow to buy the bond today).

fv = 100 (face value of bond receivable at maturity).

RATE is calculated to be 4.30%. This is the YTM.

A1 x fc =RATE(10,100*2%,-81.62,100) D E F B C A 4.30%! 1|

Bond B

YTM is calculated using RATE function in Excel :

nper = 10 (years remaining until maturity with 1 annual coupon payment each year)

pmt = 100 * 4% (annual coupon payment = face value * coupon rate)

pv = -98.39 (Current price of bond. This is entered with a negative sign because it is a cash outflow to buy the bond today).

fv = 100 (face value of bond receivable at maturity).

RATE is calculated to be 4.20%. This is the YTM.

X fc =RATE(10,100*4%,-98.39,100) А C D 2. 4.20%)

Bond C

YTM is calculated using RATE function in Excel :

nper = 10 (years remaining until maturity with 1 annual coupon payment each year)

pmt = 100 * 8% (annual coupon payment = face value * coupon rate)

pv = -133.42 (Current price of bond. This is entered with a negative sign because it is a cash outflow to buy the bond today).

fv = 100 (face value of bond receivable at maturity).

RATE is calculated to be 3.90%. This is the YTM

A3 x fc =RATE(10,100*8%,-133.42,100) D E F G B C A 3.90%! 3

Bond A has the highest YTM.

For bonds with the same maturity, those with higher coupons have lower duration, and those with lower coupons have higher duration. This is because for bonds with higher coupons, the periodic cash inflow is higher and a larger portion of the bond value is received earlier, and hence the interest rate risk is lower.

Bonds A, B, and C have the same maturity. Therefore, Bond A has the highest duration as it has the lowest coupon rate. Bond C has the lowest duration as it has the highest coupon rate